General Happiness:
* Grin
* Beam
* Laugh
* Chuckle
* Giggle
*
* More subtle/shy:
*
* More intense/forceful:
*
* More thoughtful/serene:
*
* More playful:
*
* More mischievous:
*
* More sarcastic/ironic:
*
* More concerned/sympathetic:
*
More Specific Emotions:
* Joy: radiate, exude, bask, delight
* Contentment: ease, serenity, peace, bliss
* Amusement: chortle, titter, snicker
* Triumph: exult, revel, rejoice
* Love: glow, blush, beam
* Sorrow: grimace, wince, frown
* Anger: glower, scowl, sneer
Other Options:
* Physical descriptions: curl up lips, turn up corners of mouth, show teeth
* Figurative language: light up, bloom, radiate joy
* Action verbs: laugh, giggle, chuckle, grin
The best word to use will depend on the specific situation and the emotion you want to express.